We consider a cross interpolation of high-dimensional arrays in the tensor train format. We prove that the maximum-volume choice of the interpolation sets provides the quasioptimal interpolation accuracy, that differs from the best possible accuracy by the factor which does not grow exponentially with dimension. For nested interpolation sets we prove the interpolation property and propose greedy cross interpolation algorithms. We justify the theoretical results and measure speed and accuracy of the proposed algorithm with numerical experiments.
|Number of pages||28|
|Journal||Linear Algebra and its Applications|
|Publication status||Published - 24 Jun 2014|
- High-dimensional problems
- Tensor train format
- Maximum-volume principle
- Cross interpolation